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  • 1980-1984  (636)
  • 1983  (636)
  • Engineering  (281)
  • Atomic, Molecular and Optical Physics  (251)
  • Ultrastructure  (104)
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  • 1980-1984  (636)
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  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1695-1705 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transition energy and geometry of the lowest excited (nπ*) singlet and triplet states of CO, CS, HNO, H2CO, HFCO, and F2CO molecules are calculated by CNDO/S and CNDO/2-VN-1 potential methods, and the results are compared with those of experimental and ab initio theoretical studies, wherever available. In the calculation of the vertical transition energy, the performance of the CNDO/S method is seen to be generally more satisfactory than that of the CNDO/2-VN-1 potential method, while the reverse is true for the excited-state geometry. The CNDO/S method as such fails to describe the geometry of the excited state, but a combined version (CNDO/S-2) of CNDO/S and CNDO/2, as well as the CNDO/2-VN-1 potential method is fairly successful in this regard.
    Additional Material: 1 Ill.
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  • 102
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1753-1765 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: On the basis of a high-quality LCAO MO SCF calculation, covalency versus ionicity of a Co-F bond in the CoF6(n-) complexes, where n = 4, 3, and 2, is discussed. The overlap and gross atomic populations, delocalization of certain MOS, and the charge densities in the bond region as well as around F's all indicate that the covalency increases as n decreases or the valency of Co increases in these complexes.
    Additional Material: 5 Ill.
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  • 103
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1807-1816 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In an n level quantum system there is a relation between each density operator and an element of su (n) Lie algebra. This relation is also established between Cartan's subalgebras and the complete sets of compatible observables. A scalar product is then defined in this algebra in order to introduce orthonormal bases and to simplify many calculations about expectation values of observables. Therefore simple general rules were established which show how to determine (completely or partly), from linearly independent observables, the density operator of the system.
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  • 104
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 105
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1891-1901 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The elastic forward scattering of high-energy electrons from molecules has been studied in the second Born approximation. An integral transformation has been adopted to evaluate the second Born integrals analytically without explicit use of molecular wave functions. In the high-energy limit, the differential cross section for the forward scattering is expressed in terms of electric dipole and quadrupole moments, the second moment of charge distribution with respect to the molecular center, and transition dipole moments. All these quantities are shown to be computable from molecular electron densities in the ground state.
    Additional Material: 1 Tab.
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  • 106
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    International Journal of Quantum Chemistry 23 (1983), S. 1915-1922 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We examine the short-range behavior of the spherically averaged Hartree-Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the Xαβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.
    Additional Material: 1 Tab.
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  • 107
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    International Journal of Quantum Chemistry 23 (1983), S. 1931-1944 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By the means of gauge invariance of the continuity equation Fick's law of diffusion can be extended to also comprehend the chemical reaction. In the case of first-order reactions a complete set of eigenfunctions is obtained. These solutions provide a tool for pattern recognition in biochemical and biological problems (e.g., formation of chromosome banding). The transport equation, including reactions of second order, exhibits soliton solutions describing the propagation of a kinetic process in a medium (molecular chain, fluids, etc.). A relationship to the soliton solutions of the nonlinear Schrödinger equation and Korteweg-de Vries equation of hydrodynamics is also indicated. The propagation of a reactive process (transition state) occurs in many problems of molecular biology. The Brownian motion of ions undergoing a reaction of first order in a constant magnetic field is also exactly solved.
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  • 108
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1973-1978 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the study of the ground-state binding energy of atoms, relatively more attention has been paid to the gradient expansion of the kinetic energy term of the Thomas-Fermi-Dirac model than to the gradient expansion of the exchange term of this model. Recently Shih and Shih, Murphy, and Wang have focused on this problem and calculated the first gradient expansion correction to the Dirac exchange term by making use of electron densities constructed from Hartree-Fock wave functions. In previous work, aimed to introduce the shell structure of atoms via a variational procedure using the energy density functional formalism, electron densities have been obtained for the Na atom within the Thomas-Fermi-Dirac model with and without the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. In this paper we make use of the respective electron densities and calculate the first gradient expansion corrections to the Dirac exchange term. The results show that, for the Na atom, the magnitude of this correction is about 1% of the magnitude of the total binding energy.
    Additional Material: 2 Tab.
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  • 109
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    International Journal of Quantum Chemistry 24 (1983), S. 25-60 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We discuss how the local convergence of Newton-Raphson and fixed Hessian MCSCF iterative models may be rationalized in terms of a total order of convergence in an error vector and a corresponding error term. We demonstrate that a sequence of N Newton-Raphson iterations has a total order of convergence of 2N and that a sequence of N fixed Hessian iterations has a total order of convergence of N + 1. We derive the error terms of a Newton-Raphson and a fixed Hessian sequence of iterations. We discuss the implementation of the fixed Hessian and the Newton-Raphson approaches both when linear and nonlinear transformations of the variables are carried out. Sample calculations show that insight into the structure of the local convergence of Newton-Raphson and fixed Hessian models can be based on an order of convergence and an error term analysis.
    Additional Material: 1 Ill.
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  • 110
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    International Journal of Quantum Chemistry 24 (1983), S. 113-126 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The description of electron density in solids by quantum theory and by x-ray diffraction experiments should closely coincide. A formalism for describing the electronic structure of single crystals in terms of a density matrix is presented. Iterative equations for calculating the density matrix in a basis of Bloch orbitals using measured crystallographic intensity data are derived. Numerical results are presented. The Bloch orbital formalism explicitly accounts for the mutual interaction of atoms in different unit cells, and is useful for insulators, semiconductors, and metals.
    Additional Material: 2 Tab.
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  • 111
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    International Journal of Quantum Chemistry 24 (1983), S. 135-135 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 112
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 279-306 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Löwdin basis functions are introduced and their permutation symmetry is studied in detail. A simple relation between the Löwdin basis and the orthogonal basis constructed by means of Young-Yamanouchi units is established. Both analytical and recurrence formulas for the overlap integrals of the Löwdin and some relevant auxiliary functions are derived. The symmetry of the overlap matrix of the Löwdin basis functions is briefly discussed.
    Additional Material: 1 Ill.
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  • 113
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The definitive breakdown of the CBO potential picture in consequence of the vibronic coupling of two electronic states is discussed on the basis of our model. The present treatment differs from that given in the literature.
    Additional Material: 2 Ill.
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  • 114
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    International Journal of Quantum Chemistry 24 (1983), S. 353-371 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electrostatic potentials and fields created by the thiol protease, papain, are computed on the surface envelope of the protein and in the region of its active site using a technique based on accurate multipole expansions of the electron density of appropriately chosen subunits. The effect of binding counterions to the protein is considered specifically. The possible role of the “electrostatic environment” in the functioning of the enzyme is discussed and it is found that this environment can favor the proton transfer between Cys 25 and His 159 that is thought to initiate its mode of action, but that the reasons for this appear more complicated than earlier models would suggest.
    Additional Material: 14 Ill.
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  • 115
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    International Journal of Quantum Chemistry 24 (1983), S. 411-423 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The bond length alternation problem in cyclic polyene models as described by the Pariser-Parr-Pople Hamiltonian and an empirical quasiharmonic π-core potential is investigated using the one-parameter alternant molecular orbital (AMO) method. It is shown that in contrast to the unrestricted Hartree-Fock (UHF) results, which lead to symmetric equidistant structures, the one-parameter AMO results yield bond length alternating structures similar to those obtained with the restricted HF approach. The correlation energy recovered by the AMO method is examined for the symmetric polyenes in the whole range of coupling constants for both the Pariser-Parr-Pople and Hubbard Hamiltonians and compared with exact full configuration interaction (FCI) results. For the first member of the cyclic polyene series we also compared the FCI and AMO correlation energies for different nuclear framework distortions. This comparison indicates that in contrast to the UHF results the fraction of the correlation energy recovered by the AMO approach is very uniform over the range of nuclear distortions considered. The AMO results thus strongly indicate the dimerization in the polyenic chains.
    Additional Material: 6 Ill.
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  • 116
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    International Journal of Quantum Chemistry 24 (1983), S. 435-452 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For most structures (molecules, graphs, lattices) a count of random walks for nonequivalent sites will give different numbers, particularly for walks of many steps. Occasionally one finds the same count of walks for nonequivalent sites. These have been termed “unusual walks” and have been closely examined in the case of trivalent graphs. While it remains to be understood what structural factors are critical, some regularities have been observed and are discussed. Unusual walks within a single structure signal “isospectural” points in a graph. A number of structures possessing unusual walks have been displayed, and a few constructive steps which do not alter the “unusual” characteristics of selected vertices have been indicated.
    Additional Material: 11 Ill.
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  • 117
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    International Journal of Quantum Chemistry 24 (1983), S. 523-526 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Boundaries of electronic energy level sets in the nuclear charge space wZ can be parametrized as single valued functionals for any nuclear geometry of molecules, which property, combined with the general convexity of such level sets, leads to various electronic energy inequalities.
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  • 118
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    International Journal of Quantum Chemistry 24 (1983), S. 593-602 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In connection with the reinterpretation of Hund's multiplicity rules for molecules, a detailed study has been made of the energy differences in the total energy and its components for the triplet and singlet Πu states of the hydrogen molecule and the analogous states of the four- and six-membered hydrogen atom rings. For the hydrogen molecule, both SCF and CI studies indicated that the outer electron is considerably more contracted in the triplet than in the singlet state. In both approximations, the energy difference is dominated for all bond distances of chemical and physical significance by the electron-nuclear attraction component and not by the electron repulsion component as predicted by simple first-order perturbation theory. Although the correlation energy for each of the states is of the same magnitude as the energy differences considered here, the difference of the correlation energies is much smaller. It had little effect on the qualitative differences between these states of the hydrogen molecule. For the four- and six-membered rings, SCF studies were made on the lowest singlet and triplet states where one electron was promoted from the σg to a Πu orbital. Even though the coupled electrons were more delocalized in these cases, the electron repulsion became relatively more important. However in all cases, the lower state had the highest electron repulsion energy and lower electron-nuclear attraction. The triplet state continued to have the more contracted outer open-shell orbital.
    Additional Material: 4 Ill.
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  • 119
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    International Journal of Quantum Chemistry 24 (1983), S. 633-649 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Basic integrals arising in the momentum space formulation of the van der Waals forces are derived for arbitrary two atoms. These integrals are essentially the matrix elements of the Fourier transformed Coulomb operator and the Fourier transformed square of the Coulomb operator between any two Slater orbitals. The derivation is completely analytic and the results are expressed as finite series expansions in terms of auxiliary integrals. Recursion relations among the auxiliary integrals are developed.
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  • 120
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    International Journal of Quantum Chemistry 24 (1983), S. 729-745 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Every Slater determinant D may be uniquely analyzed in terms of spin components Dl = OlD which are pure spin eigenfunctions, so that S2Dl = l(l+1)D. Every component Dl = OlD may in turn be written as a sum of symmetric combinations of Slater determinants, Tk = [αμ-kβk‖αkβν-k], and the coefficients ck(l) in the expansion OlD = ∑k ck(l) Tk are known as the “Sanibel coefficients.” By using the relation S2Dl = l(l+1)D, a recursion formula for the coefficients ck(l) is derived, which is then explicitly solved in the special case when Sz has the pure quantum number m = 0.
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  • 121
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    International Journal of Quantum Chemistry 24 (1983), S. 697-706 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The concept of atomic valency is looked at as a specific response of an atomic system to an arbitrary environment. It is shown, on the basis of a mathematical result in group actions theory, how valency might be related both to previously found Hartree-Fock deformed states and to the isotropy groups (up to a conjugation) of the extrema of the electronic energy functional.
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  • 122
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    International Journal of Quantum Chemistry 23 (1983), S. vii 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 123
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    International Journal of Quantum Chemistry 23 (1983), S. 65-70 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The use of the antisymmetrized geminal power (AGP) consistent reference state for RPA polarization propagator calculations is explored. Illustrative applications to the three lowest electronic states (3B1, 1A1, and 1B1) of the methylene radical are reported with comparisons to other theoretical methods and experiment.
    Additional Material: 1 Ill.
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  • 124
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    International Journal of Quantum Chemistry 23 (1983), S. 235-248 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Hartree-Fock method (standard Roothaan closed-shell HF-LCAO theory) and the Hartree-Fock-Slater method (restricted HFS-LCAO-DV method developed by Baerends and Ros) have been compared with emphasis on the respective one-electron equations and on the matrix elements of the respective Fock operators. Using the same STO basis in the two cases, the matrix elements of the Fock operators and of their separate one-electron, Coulomb, and exchange contributions have been calculated for the same orbitals and density of the ground state of the diatomic molecule ZnO. The effects of methodical (exchange potential) and numerical (DV method, density fit) differences between the HF and HFS methods on the various matrix elements have been analyzed. As expected the methodical effect prevails and is responsible for the higher (less negative) values of the matrix elements of the HFS Fock operator compared to those of the HF Fock operator. Numerical effects are observable also and are caused by the difference in integration procedures (DV method), not by the density fit.
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  • 125
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    International Journal of Quantum Chemistry 23 (1983), S. 99-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Hilbert space may be regarded as a convenient standard approximation by interpolation and extrapolation to a unitary space, in general decomposable into a sum of semisimple spaces. In the limit we expect a particle theory expanded in powers of h according to the number of interacting particles. In the classical limit h tending to zero, phase space, with equations of motion reducible to Hamiltonian form, replaces Hilbert space. The modification of states by observing them is taken care of by considering probability distributions of petty ensembles. If the equations for any single observer can be made autonomous by replacing empirical time by universal time with an arrow we have a causal system. We then obtain the relation between probability and negentropy required for the second law of thermodynamics. An approximate Newtonian theory provides proximate particles with internal and external variables and admits the Poincaré group. For the internal variables we have approximately the Breit interaction. For the external variables we have equivalence for observers of the homogeneous Lorentz group of relativity. We introduce grand ensembles of ultimate particles, and nebulae as proximate particles in the large. We assume the Einstein principle of equivalence for the ten parameter set of observers suggested by relativity and suppose the second law of thermodynamics holds for each observer. The Einstein law of gravitation follows in classical theory to the order of the reciprocal of the large constant, in general with positive natural curvature as well as that corresponding to mass. Replacing particle interactions by fields we include them in classical theory.
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  • 126
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    International Journal of Quantum Chemistry 23 (1983), S. 147-167 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree-Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.
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  • 127
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    International Journal of Quantum Chemistry 23 (1983), S. 309-317 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A two-dimensional fully numerical relaxation approach is presented for the electronic Schrödinger equation of linear molecules. The method is tested on the lowest σ, π, δ, and φ states of H2+ and HeH2+. About 10-figure accuracy is obtained for the orbital energies. Seven-point numerical formulas are given for first and second derivatives.
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  • 128
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    International Journal of Quantum Chemistry 23 (1983) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 129
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    International Journal of Quantum Chemistry 23 (1983), S. 369-377 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quantum mechanics is a remarkable formalism for studying problems in the microscopic domain, and nobody has reasonably contested its power. Nevertheless, in spite of the many interpretations which have been proposed, its true meaning is far from being clear. The aim of this preliminary paper is to show that it is possible to conceive within a classical framework an interpretation of quantum mechanics and to make its limits of validity precise.
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  • 130
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    International Journal of Quantum Chemistry 23 (1983), S. 341-363 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule - a factor completely overlooked in the usual scheme of calculations.
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  • 131
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    International Journal of Quantum Chemistry 23 (1983), S. 417-423 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical expressions for the square of the spherical average of Fourier transforms of Gaussian type orbitals (GTO's) are given. A direct application of these expressions to the calculation of molecular photoionization cross sections is considered under the generalized sudden (GSA) and dipole (DA) Approximations. Numerical calculations were done on the CO molecule using bound orbitals obtained by ab initio LCAO-MO calculations with Gaussian basis sets. The results are in good agreement with experiments. Those obtained by the GSA method however, suggest a limitation in its use: the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals. Applications to other molecules are immediate.
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  • 132
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multiple-scattering-Xα (MS-Xα) calculations have been performed on IrCl63-, IrCl62-, and WO66- clusters. Relativistic calculations have been performed by the inclusion of the approximation of Wood and Boring in the MS-Xα method, i.e., mass-velocity and Darwin terms are taken into account self-consistently, while the effects of the spin-orbit operator are estimated by first-order perturbation theory. The strong contraction of s and p orbitals can be seen on selected displays of radial wave functions and significant changes in the energy diagrams between the nonrelativistic and the relativistic calculations can be obtained. The comparison with photoemission spectra clearly shows the necessity of including relativistic corrections in the calculations. The calculated spin-orbit parameters are in agreement with experiment for core levels, while a strong dependence of the spin-orbit parameters on the one electron energies is pointed out; this dependance is unconnected from the atomic contributions to the molecular orbitals.
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  • 133
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    International Journal of Quantum Chemistry 23 (1983), S. 465-472 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multiconfiguration (MC) SCF calculations are reported for CO2 for bond angles between 60° and 180°. The ground state configuration is found to be …5a124b22∣b12∣a22 for small bending angles and …6a123b22∣b12∣a22 for large bending angles, the change in ground state character occurring at a bond angle of about 100°. The force constant for bending obtained from the MC-SCF function is about 8.0% lower than the corresponding SCF value, and in considerably better agreement with experiment.
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  • 134
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    International Journal of Quantum Chemistry 23 (1983), S. 497-505 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using some properties of the Bessel functions the algebraic representation of the Nakajima-Zwanzig generalized master equation was derived. This representation makes possible the calculation of the memory functions in terms of the probabilities. Using this approach, the formulas for the memory functions giving their dependence on the eigenvalues and eigenvectors of the corresponding stationary Schrödinger equation are given and discussed in detail.
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  • 135
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    International Journal of Quantum Chemistry 23 (1983), S. 535-542 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A semiempirical SCF MO method has been developed in which the wave function of a composite molecule is written as a linear combination of localized fragment orbitals and which is formulated such that strictly transferable empirical data for the fragments may be introduced into the calculation. Results of FIM calculations in the CNDO/2 approximation for a number of R—X molecules with R = alkyl and X = F, OH, NH2, and CH3 are presented and used to illustrate the possibilities and limitations of the method.
    Additional Material: 1 Ill.
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  • 136
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    International Journal of Quantum Chemistry 23 (1983), S. 561-566 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We outline a theory of UV and higher-energy photoemission spectroscopy of chemisorbed atoms, that aims at the accurate calculation of inner electron binding energies and photoabsorption cross sections by including solid state and localized relativistic and correlation effects. It is based on an “atom on (in) solids” approach where one first extracts a surface potential and then uses it in a coupled Hartree-Fock theory to obtain self-consistently the shifts and splittings of atomic levels. A first application of this theoretical program has been carried out on Na on the Al(100) system, by calculating from first principles the binding energies of the Na 1s and 2s electrons. For a coverage of 1.23 × 1014 adatoms/cm2 we find BE(1s) = 1075.2 eV and BE(2s) = 66.2 eV. Also, the Na 2p orbitals are found to split in the cylindrical symmetry by about 0.2 eV.
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  • 137
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    International Journal of Quantum Chemistry 23 (1983), S. 633-637 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theory for nuclear shielding including electron correlation effect is derived and applied to the hydrogen fluoride molecule. It is shown that about 20% of the paramagnetic contribution to nuclear shielding at nucleus F is due to electron correlation. Inclusion of electron correlation effect greatly improves the calculated values toward the experimental ones.
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  • 138
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    International Journal of Quantum Chemistry 23 (1983), S. 679-686 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Heats of atomization for a range of conjugated molecules containing nitrogen or oxygen are calculated by a semiempirical method that combines some features of both the MO and VB theories. The π ground state of each conjugated molecule is represented as a linear combination of Kekulé structures. Unlike in the VB theory, each Kekulé structure is a determinant containing bond orbitals. Here experimental heats of atomization are reproduced approximately as well as by the more sophisticated SCF-MO approach. The use of this method is, however, much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.
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  • 139
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    International Journal of Quantum Chemistry 23 (1983), S. 713-722 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A computer-oriented algorithm is developed for identification and enumeration of carcinogenic bay regions in benzenoid hydrocarbons. The results are reported for geometrically planar benzenoid systems up to ten fused rings. They fully agree with those obtained in a different way by Balasubramanian et al. The advantage of the proposed method is that we can display all planar benzenoid structures and identify the carcinogenic bays in each of them.
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  • 140
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    International Journal of Quantum Chemistry 23 (1983), S. 753-764 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Proton transfer between N and O in the hydrogen-bonded system (H3NHOH2)+ is studied by ab initio molecular orbital methods. Potential energy curves are calculated at the hartree-Fock level using the 4-31G basis set for hydrogen bond lengths R(NO) varying from the equilibrium value of 2.664 to 3.10 Å. Short hydrogen bonds are associated with asymmetric single-well potentials in which the minimum corresponds to the NH—O configuration. For longer R(NO) separations, the potential is of double-well form, including both N—HO and NH—O as minima. It is found that the height of the energy barrier to proton transfer is sensitive to both stretches and bends of the hydrogen bond. Continuous changes in the electron density are monitored at various stages of proton transfer via density difference maps and Mulliken population analyses. The initial loss of density from the proton-accepting molecule during the first half of the transfer is accelerated during the second half. A correlation is drawn between the energetics of transfer in a number of systems and the net charge lost by the proton-acceptor group.
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  • 141
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    International Journal of Quantum Chemistry 23 (1983), S. v 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
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  • 142
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    International Journal of Quantum Chemistry 23 (1983), S. 821-834 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new technique for a simple and efficient treatment of intermolecular interactions is proposed and tested. The method is based on an approximation of the first order SCF term ESCF(1) which is the most structured contribution to the total interaction. ESCF(1) is represented by a site-site potential V of (exp, 1/R)-type, which accounts for the exchange plus penetration and the long range Coulomb forces (by means of a point charge model). The individual contributions to V are obtained by means of combination rules from corresponding site parameters of interacting molecules. The site parameters are consequently molecular and not intermolecular properties and can conveniently be determined by probing a molecule with appropriate test particles. Site parameters are reported for He, Ne, Ar, N2, CO, CO2, CS2, and HCl. Comprisons show close agreement of V with ESCF(1) which in turn is close to ΔESCF if polarization and charge transfer effects are small.
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  • 143
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    International Journal of Quantum Chemistry 23 (1983), S. 855-863 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical models for reductive elimination from transition metal containing molecules have been studied using large scale contracted CI calculations. Four different models were treated, namely, NiH2, PdH2, Ni(CH3)2, and Pd(H2O)2H2, in order to study the effects of adding ligands, exchanging hydrogens with methyl groups, and comparing nickel and palladium. The most interesting result already appeared for the simplest system NiH2. A closed-shell-type 1A1 state with a small bond angle of only 57° is bound compared to Ni and H2 with only a very small barrier for formation. The bond distance is short, shorter than in NiH, and the d orbitals are strongly involved in the binding. The hydrogen atoms bind both to nickel and to each other. With methyl groups rather than hydrogens, this double sided bonding situation is destroyed and Ni(CH3)2 has a negative binding energy with the carbon bonds pointing towards nickel. For PdH2 only a weakly bound complex between an essentially unchanged H2 and Pd was found. The bond distance is very long. Adding H2O ligands to Pd shortens the bond distance and significantly opens up the bond angle. The methods used in the investigation and the chemical implications of the results are discussed.
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  • 144
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    International Journal of Quantum Chemistry 23 (1983), S. 945-952 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The title complex is considered a model for the interaction of catecholamine-type ligands with anionogenic sites of receptors. It is usually assumed that the ligands interact in the protonated form, but there is no direct evidence of this. Model computations of proton transfer processes should contribute to the elucidation of this important problem. As a first step in this direction we have made computations in the STO-4G base of the interaction energies, molecular electrostatic potentials, the proton potential curves, and the Mulliken population for three different arrangements of the acid and base molecules. Proton potential functions have also been computed for the complexes with two water molecules attached to the acid. The deeper potential well is nearer to the carboxylic oxygen in all cases examined.
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  • 145
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    International Journal of Quantum Chemistry 23 (1983), S. 921-943 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The history of important developments in the theory of hybrid bond orbitals and its application in valence-bond theory is reviewed. One of the salient points, the bond strength of a hybrid orbital, is defined as the value of the angular part of the orbital along the bond direction. Characteristic bond angles corresponding to maxima in the bond strength are presented for various basis sets. In order to alleviate computational difficulties in determining the bond strength for complex systems, an approximation to it, the pair-defect-sum approximation, is described. The results of an exhaustive test of the validity of this approximation are presented. Applicaitions of these ideas to coordinate chemistry are provided. Finally, the case is made for the continued viability of valence-bond theory in this age of omnipresent computer terminals.
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  • 146
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    International Journal of Quantum Chemistry 23 (1983), S. 1025-1032 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Fluorescence studies of Cu+ and Ag+ impurity centers embedded in NaCl are reported. The multiple scattering Xα method is used to describe the electronic structure of these ions in NaCl matrix. It is shown that taking into account the external lattice potential is necessary to obtain good results which can be compared to experiment. This has been done through the computation of an embedded NaCl65- cluster potential. Moreover, in NaCl:Ag+, it is also necessary to include relativistic corrections in order to obtain a reliable energy diagram. This is easily done by use of the Wood Hamiltonian, which allows the self-consistent inclusion of Darwin and mass-velocity terms in MS Xα codes. A good quantitative agreement with experiment is finally obtained for the optical excitations and the emission mechanism of the luminescent centers. The metal-chlorine distance is predicted slightly larger than the NaCl bulk value and the harmonic force constant of the a1g vibrational breathing deformation of the cluster is calculated and found in good agreement within experiment. For the first time the Stoke shift of such systems is evaluated.
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  • 147
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    International Journal of Quantum Chemistry 23 (1983), S. 1065-1072 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the case of conjugated polyenic chains (polyacetylene), the relationships between the long- (or short-) range nature of the restricted Hartree-Fock exchange interaction, the role of correlation effects, and the size of energy gaps are illustrated.
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  • 148
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    International Journal of Quantum Chemistry 23 (1983), S. 1057-1063 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have recently produced a Lifson-Warshel force field for the silicon crystal. This field, that goes further than the harmonic approximation, is particularly adapted for the calculation of defect structures. It requires five free parameters, but one of them in the field already produced, the linear bending term, is significant for the perfect lattice structure only and should be eliminated in dealing with defect structures. Also, one of the fixed parameters can be adjusted to fit precisely the experimental value of the stacking fault energy. We show that an excellent fitting of the phonon dispersion curves, in the least squares sense, is obtained with the parameters thus changed. We illustrate the use of this field in discussing the problem of reconstruction of the 90° partial dislocation in silicon.
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  • 149
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    International Journal of Quantum Chemistry 23 (1983), S. xi 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 150
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    International Journal of Quantum Chemistry 23 (1983), S. 1135-1153 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three different algorithms for the calculation of many center electron-repulsion integrals are discussed, all of which are considered to be economic in terms of the number of arithmetic operations. The common features of the algorithms are as follows: Cartesian Gaussian functions are used, integrals are calculated by blocks (a block being defined as the set of integrals obtainable from four given exponents on four given centers), and functions may be adopted to R(3). Adaption to molecular point group symmetry is not considered. Tables are given showing the minimum number of operations for a selection of block types allowing one to identify the theoretically most economic, and the corresponding salient features. Comments concerning the computer implementations are also given both on sealar and vector processors. In particular, the Cyber 205 is considered, a vector processor on which we have implemented what we believe to be the most efficient algorithm.
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  • 151
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    International Journal of Quantum Chemistry 23 (1983), S. 1121-1133 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Attempting to explain the differences in the pharmacological profiles of the isomeric monohydroxy-and dihydroxy-2-aminotetralins (DHAT) which are potent dopaminergic agonists we have calculated the conformational energies of 2-aminotetralin and its N,N-dipropyl derivative using the QCFF/Pi and PCILO methods. Molecular electrostatic potential (MEP) maps based on ab initio (STO-3G) wave functions were computed for both dihydroxytetralins. Root-mean-square (rms) deviations from steric congruence between the enantiomeric 5,6- and 6,7-DHAT based either on atomic centers or on the minima in MEP near the putative points of attachment to the receptor are small, but may nevertheless be sufficient to cause differences in activity on subtypes of the dopamine receptor. N,N-dipropyl substitution influences the conformational energies of the skeleton and the preferences in the orientation of the propyl groups in the isomeric DHAT may be important for the interaction with the receptor. The HOMO energies of the isomeric HAT and DHAT do not correlate with their potencies.
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  • 152
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    International Journal of Quantum Chemistry 23 (1983), S. 1091-1100 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum dynamical behavior of the Van der Waals molecule (N2)2 and that of the ordered α and γ phases of solid N2 have recently been calculated, starting from the same ab initio N2—N2 potential. By interpreting the results of these calculations we try to improve our understanding of the libration/internal rotation motions of the N2 monomers and the orientational order-disorder (α-β) phase transition. Some new results are presented and further (mean-field and libron-model) calculations are proposed which assess explicitly the intermolecular pair correlation effects caused by the anisotropic interaction potential.
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  • 153
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    International Journal of Quantum Chemistry 23 (1983), S. ix 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 154
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    International Journal of Quantum Chemistry 23 (1983), S. 1165-1177 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Semiempirical methods used in cluster-type calculations must be applicable for calculating ionization potentials (“valence band”) and electronic transitions (“gap”). CNDO/S seems to be an appropriate choice for this purpose. However, the solids of main interest (as, e.g., diamond and silica) contain saturated bonds for which the original parametrization does not work well. A new set of parameters was determined for C, O, and Si by fitting them to vertical ionization potentials and to singlet electronic transitions of their saturated molecules. The transferability of the parameters were also checked. By these parameters a successful description of the electronic structures of diamond and silica became possible.
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  • 155
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    International Journal of Quantum Chemistry 23 (1983), S. 1201-1207 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An all-electron ab initio LCAO-MO SCF calculation has been carried out for the electronic structure of small copper clusters (Cun, n = 2-6). The basis set superposition error occurring in the calculation, the equilibrium configuration of Cu3, the bond energy in the clusters, and the localized d-hole in excited and ionized states of Cu2 are closely examined.
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  • 156
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio self-consistent calculation has been carried out for the electronic properties of BaC6. Energy bands and charge densities are presented for BaC6 and compared with those of LiC6. The results show that the band originating from Ba states has a mixture of s and d character and the d component hybridizes appreciably with the π bands of graphite. The Fermi level intersects this band as well as the graphite π bands, giving rise to a complicated Fermi surface with several types of carriers. Depending on the type of volumetric partitioning, the charge transfer from Ba to graphite layers is determined to be between 0.7 and 1.0 electron per Ba atom. The calculated results are consistent with available transport and optical measurements.
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  • 157
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    International Journal of Quantum Chemistry 23 (1983), S. 1305-1316 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Expressions needed in INDO calculations for compounds containing 4f elements were derived and an INDO program suitable for lanthanoid compounds was written and tested. Electronic structure of LnF3 and paramagnetic shift of NMR spectra of LnF85- were studied.
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  • 158
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    International Journal of Quantum Chemistry 23 (1983), S. 1517-1528 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A magnetic transition state model is developed for the description of magnetic interactions and magnetic phase transitions in solids. The model is based on the one-electron Xα molecular orbital calculations of clusters embedded in crystal lattice and allows quantitative investigations of magnetic interactions in d and f metals, their alloys, and compounds. The energies of local spin excitations and magnetic transition temperatures are calculated for a series of systems with the electronic states localized to a different extent. The effects of covalent bonding are introduced directly into magnetic parameters calculations and appear to be of crucial importance. Magnetic properties of some disordered alloys are considered basing on the results of Xα cluster calculations performed. In the low concentration limit, the local moment existence problem is being discussed. The dependence of magnetic properties upon concentration is considered. The results of calculations allow to give the reasonable interpretation of the experimental data available and show good possibilities of the cluster model in the description of magnetic effects in solids.
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  • 159
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    International Journal of Quantum Chemistry 23 (1983), S. 1553-1561 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A unimolecular process is considered that was treated experimentally as a concerted one; however, subsequent quantum-chemical analysis has proved that the process is realized via an intermediate (double sequential isomerism of activated complexes). The intermediate is supposed to contribute directly to values of the primary observed data (e.g., spectral absorbances). Within this approach of interfering intermediate any degree of this interference is allowed including the limit case of noninterfering intermediate serving as a reference standard. A technique is suggested enabling correct comparison of the quantum-chemical outputs with the experimental overall values for rate constants and activation enthalpy and entropy. The technique employs mere amount of information currently obtainable from quantum-chemical study of a rate process (i.e., representation of potential energy hypersurface by its stationary points and activated-complex theory). Properties of the derived formulae are illustrated with model examples. The results are important for meaningful comparison of experimental and theoretical data in the case of processes with sequential isomerism of activated complexes disclosed only theoretically.
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  • 160
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    International Journal of Quantum Chemistry 23 (1983), S. 1589-1595 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: From theoretical considerations, three types of coherent excitations of biological systems have been suggested: (i) vibrations of membranes and of proteins with frequencies above 109 Hz; (ii) near static excitation of a highly polar metastable state; and (iii) low frequency periodic enzyme reactions. Recent experimental evidence is discussed.
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  • 161
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    International Journal of Quantum Chemistry 23 (1983), S. 1611-1625 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relative importance of purely nonadditive three-body terms in solvated systems is assessed through ab initio LCAO-MO-SCF studies of hydrogen bonded structures containing two or more water molecules plus a solvate species. Among the latter the cases of Li+, Ca2+, and Mg2+ ions (of biological interest for aminoacid release processes in membrane transport) and of HDS molecules (of industrial importance in processes for the production of heavy water) are studied.
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  • 162
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    International Journal of Quantum Chemistry 23 (1983), S. 1677-1677 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 163
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    International Journal of Quantum Chemistry 23 (1983), S. 1679-1681 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 164
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    International Journal of Quantum Chemistry 23 (1983), S. 1693-1693 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 165
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    International Journal of Quantum Chemistry 23 (1983), S. 1739-1752 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio SCF MO calculations have been carried out on benzene + TCNE (tetracyanoethylene) and naphthalene + TCNE complexes with the STO-3G, STO-3G π-split (STO-3G for π orbitals and a split basis for π orbitals), and 4-31G basis sets. The interaction energy, gross charges, dipole moment, and the electron density in the middle plane of the complexes have also been evaluated. The STO-3G π-split basis set is appropriate for the calculation of large π-π stacking complexes from two points of view, production of reliable results and ease of computations. The approximation scheme based on the semiorthogonalized orgitals is revealed to be very efficient to save CPU time and storage in such calculations. The stable conformation and the charge-transfer interaction of the two complexes are discussed on the basis of the calculated quantities.
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  • 166
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    International Journal of Quantum Chemistry 23 (1983), S. 1803-1806 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A number of trimers of water molecules have been computed with an extended basis set in the Hartree-Fock and in the direct CI approximations. It has been verified that the three-body interaction energy can be calculated within the Hartree-Fock method. Therefore, the correlation corrections to the Hartree-Fock level are essentially additive and do not contribute significantly to three-body effects.
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  • 167
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    International Journal of Quantum Chemistry 23 (1983), S. 1829-1841 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The definition of the cyclic polynomial of conjugated hydrocarbons is offered. The combinatorial characteristics of this polynomial are investigated. The most important property of the cyclic polynomial is that it can be used for enumeration of conjugated circuits.
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  • 168
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    International Journal of Quantum Chemistry 23 (1983), S. 1903-1914 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Vertical ionization potentials for core orbitals of HF, H2O, and CO are calculated with the ab initio transition operator method. The results are improved by third-order Rayleigh-Schrödinger perturbation theory. The effect of basis sets is also investigated. The computed core-electron binding energies are compared with the experimental values and with those obtained by other theoretical methods. The comparison shows that the present approach leads to reliable core ionization energies, the average absolute deviation from experiment being only 0.4 eV for the cases studied.
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  • 169
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    International Journal of Quantum Chemistry 23 (1983), S. 1923-1930 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An attempt to classify various types of avoided surface crossings originally discussed by Salem and co-workers is presented. From the present scheme, an order-of-forbiddenness criterion regarding reactivity is established from a consideration of electron and orbital counting. Since the new classification is qualitatively related to the energy gap created in the avoided crossing, the classification appears to be more systematic and informative. Energy transfer processes involved in electronically excited states may also be rationalized by such an application. Three major mechanistic types are distinguished: concerted two-electron process, concerted one-electron process, and stepwise one-electron process involving an ionic-pair intermediate.
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  • 170
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    International Journal of Quantum Chemistry 24 (1983) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 171
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    International Journal of Quantum Chemistry 24 (1983), S. 19-23 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure for generating basis sets for diatomic molecule electronic structure calculations is described. In essence, this procedure maps the results of nearly exact numerical Hartree-Fock calculations into basis set form. Two applications of the procedure are proposed: (a) generation of very high accuracy basis sets, and (b) investigation of basis sets for unusual systems. The latter application is illustrated by some results for diatomic anions.
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  • 172
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    International Journal of Quantum Chemistry 24 (1983), S. 1-18 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical properties of hydrogen-like atomic orbitals (HAO) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.
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  • 173
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    International Journal of Quantum Chemistry 24 (1983), S. 65-77 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method for nonadiabatic many-particle quantum-mechanical calculations is described and illustrated for the special case of three particles. The method uses a basis of explicitly correlated Singer-type exponential quadratic function (polymals) of the internal degrees of freedom. Rigorous symmetry states are projected from the basis: linear momentum of the center of mass, total angular momentum, and permutational symmetry under interchange of indistinguishable particles. The nonadiabatic wave functions are interpreted via purely quantum-mechanical criteria of interparticle correlation as measured by average values of powers of interparticle distances and angles. The illustrations are made on H2+ which is easily treated in the Born-Oppenheimer and adiabatic approximations, on helium, muonic helium, and on (e+, e-, e+) which are poorly described in adiabatic methods. The ground and lowest bound excited states of these systems are studied with up to 256 tempered Singer polymals for which we find energies too high by 0.0011 a.u. in H2+, 0.0017 a.u. in muonic helium, 0.0009 a.u. in 4He, and 0.0002 a.u. in (e+, e-, e+); the corresponding relative errors are 1800, 4, 300, and 200 ppm, respectively.
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  • 174
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    International Journal of Quantum Chemistry 23 (1983), S. 1979-1987 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A one-electron correlation operator is introduced into the Hartree-Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree-Fock equation are equal to that from second-order perturbation of Hartree-Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.
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  • 175
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    International Journal of Quantum Chemistry 24 (1983), S. 61-64 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Recently, using the Na atom as an example, Csavinszky has introduced the shell structure into the Thomas-Fermi-Dirac energy-density functional with the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. Also recently, two rigorous lower bounds to the Weizsäcker correction in atoms of spherical symmetry have been derived by Gadre and Pathak. The present work investigates the magnitudes of the lower bounds in statistical models of the Na atom with shell structure.
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  • 176
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    International Journal of Quantum Chemistry 24 (1983), S. 127-130 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 177
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    International Journal of Quantum Chemistry 24 (1983), S. 137-137 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 178
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    International Journal of Quantum Chemistry 24 (1983), S. 85-96 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The equilibrium Co—F bond distance and the a1g vibrational frequency of CoF6n- complexes (n = 4, 3, and 2) in crystals were investigated from a theoretical point of view. Ab initio SCF MO calculations were performed for the isolated CoF6n- complexes in order to obtain the potential energy curves against the Co—F distance. These potential energy curves were improved by considering the effect of the surrounding ions. It is shown that the effects of the next-nearest neighbors (eight K+ ions) and the next-next-nearest neighbors (six Co2+ ions) are very important in determining these properties for “ionic” KCoF3 crystal. On the other hand, for Cs2CoF6 crystal, in which the Co—F bond has considerable degree of covalency, the shape of the potential energy curve is almost completely determined by the nonelectrostatic component of the intramolecular interaction of the isolated CoF62- unit.
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  • 179
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    International Journal of Quantum Chemistry 24 (1983), S. 131-133 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
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  • 180
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    International Journal of Quantum Chemistry 24 (1983), S. 243-277 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper has three aims: (i) To discuss some of the mathematical connections between N-particle wave functions ψ and their single-particle densities ρ (x). (ii) To establish some of the mathematical underpinnings of “universal density functional” theory for the ground state energy as begun by Hohenberg and Kohn. We show that the HK functional is not defined for all ρ and we present several ways around this difficulty. Several less obvious problems remain, however. (iii) Since the functional mentioned above is not computable, we review examples of explicit functionals that have the virtue of yielding rigorous bounds to the energy.
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  • 181
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  • 182
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    International Journal of Quantum Chemistry 24 (1983), S. 491-507 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Computations are performed on the interaction specificities of tetramethylammonium (TMA) for double-stranded oligonucleotides held in the B conformation. The effects of base sequence and chain length are investigated. In the short oligomers (helices formed from dinucleoside monophosphates and trinucleoside diphosphates), the interaction energies of TMA are larger in the major groove of (dG)n · (dC)n than in the minor groove of either (dA)n · (dT)n or (dA - dT)n. Upon lengthening the oligomers, and owing to the gradual shaping of the grooves of the helix and cumulative effect of the phosphates, TMA is shown to increasingly favor the minor groove of (dA)n · (dT)n with respect to the major groove of (dG)n · (dC)n, with a sizeable energy difference computed at the pentanucleoside hexaphosphate level. The binding of TMA in the minor groove of (dA)n · (dT)n involves stabilizing contacts with several sites, on the bases and on the deoxyriboses. Configurations locating the cation closer to the thymine strand are slightly preferred over configurations locating it closer to the adenine strand.
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  • 183
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    International Journal of Quantum Chemistry 24 (1983), S. 509-519 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper reports a study on which behavior of the Hamiltonian gives rise to violation of the noncrossing rule. In principle, the noncrossing rule may be violated when a special symmetry other than spatial and spin symmetries is present or there exists the so-called alternance, which corresponds to a Hamiltonian in a real vector space anticommuting with a Hermitian operator. In the HMO models for pericyclic reactions, violations due to special symmetry or alternance have been found. The [m,n] supra-antara cycloadditions have no symmetry in the traditional sense, but have special symmetry leading to the existence of crossings in the correlation diagram. Alternance results in one crossing in the middle of the correlation diagram of a forbidden pericyclic reaction with intermediate states in the form of even alternant hydrocarbon. For the reactions with intermediate states in the form of odd alternant hydrocarbon such as [2,4]-cycloaddition of an allyl cation or an allyl anion to butadiene, there should be no crossing in the correlation diagrams, and both the supra-supra and the supra-antara processes are predicted to be allowed. Such a prediction is beyond the Woodward-Hoffmann rule.
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  • 184
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    International Journal of Quantum Chemistry 24 (1983), S. 527-550 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expectation values 〈rk〉 (-2 ≤ k ≤ 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree-Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.
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  • 185
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    International Journal of Quantum Chemistry 24 (1983), S. 603-621 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new Tamm-Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm-Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H4 system with D2h and D4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm-Dancoff correction improves the result as much as the double excitation CI. The Tamm-Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.
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    International Journal of Quantum Chemistry 24 (1983), S. 687-695 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quasi-Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH3)7, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.
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  • 187
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    International Journal of Quantum Chemistry 24 (1983), S. 623-626 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The nuclear magnetic shielding and magnetizability tensors for the BH molecule are calculated by the coupled-Hartree-Fock method and many-body perturbation theory. As in the case of H2, HF, and F2, the second-order non-CHF diagrams make an inappreciable contribution.
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  • 188
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    International Journal of Quantum Chemistry 24 (1983), S. 651-685 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The molecular density required to give the correct values for one-electron properties is rarely given by wave functions obtained from variation methods based on the total energy or the eigenvalues. Perhaps if we knew how the density should be shaped in any particular volume to fit a particular property, the whole molecular density might then be properly described to fit the whole volume. The secant-parametrization procedure is used to constrain minimum basis set RHF wave functions for N2, FH, CO, and LiH to determine the effects of different constraints on RHF wave functions, and to see how constraints improve the quality of small basis set RHF wave functions. One-electron property expectation values, energies, and unweighted and property weighted populations and electron density difference profiles are used to analyze the constrained wavefunctions. With the information from the constrained wave functions it should be possible to select a LCAO-CI basis and states to give the correct density for all properties. This should map onto the constrained wave function in the region of the constraint and at the same time minimize the energy of the total molecular wave function. Such a density would be suitable for the density analyses favored by Bader and Nguyen-Dang [Adv. Quantum Chem. 14, 113 (1981)], Mezey [Theor. Chim. Acta 54, 95 (1980); 58, 309 (1981); 59, 321 (1981)], and March [Theoretical Chemistry (Royal Society of Chemistry, London, 1981), Vol. 4, p. 158], and show the real atom needed to generate the molecule.
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    International Journal of Quantum Chemistry 24 (1983), S. 767-771 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energetics of rotation about the N—C′(ω); N—Cα(ϕ), and Cα—C′(φ) bonds of the peptide unit have been investigated in the pseudo-FSGO fragment scheme on model compounds formamide and N-methylacetamide. The results indicated that the position of the minimum in ω is in the near vicinity of 0°, i.e., the planar arrangement of the peptide unit. The minimum in ϕ (C′—N—Cα—H) has been found to be 180° and in ψ(H—Cα—C′—N) to be 60°, in good agreement with PCILO and Gaussian-70 results.
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    International Journal of Quantum Chemistry 23 (1983) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    International Journal of Quantum Chemistry 23 (1983), S. 1-26 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new density-functional equation is suggested for the direct calculation of electron density ρ(r) in many-electron systems. This employs a kinetic energy functional T2 + f(r)T0, where T2 is the original Weizsäcker correction, T0 is the Thomas-Fermi term, and f(r) is a correction factor that depends on both r and the number of electrons N. Using the Hartree-Fock relation between the kinetic and the exchange energy density, and a nonlocal approximation to the latter, the kinetic energy-density functional is written (in a.u.) \documentclass{article}\pagestyle{empty}\begin{document}$$ t[\rho] = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}\nabla ^2 \rho + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 8}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$8$}}(\nabla \rho \cdot \nabla \rho)/\rho + C_k f({\bf r})\rho ^{5/3}, $$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$ C_k = {\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}(3\pi ^2)^{2/3} $\end{document}. Incorporating the above expression in the total energy density functional and minimizing the latter subject to N representability conditions for ρ(r) result in an Euler-Lagrange nonlinear second-order differential equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \left[{ - {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\nabla ^2 + v_{{\rm nuc}} ({\bf r}) + v_{{\rm cou}} ({\bf r}) + v_{XC} ({\bf r}) + {\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 3}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$3$}}C_k g({\bf r})\rho ^{2/3}} \right]\phi ({\bf r}) = \mu \phi ({\bf r}) $$\end{document} where μ is the chemical potential, we have ρ(r) = |φ(r)|2, and g(r) is related to f(r). Numerical solutions of the above equation for Ne, Ar, Kr, and Xe, by modeling f(r) and g(r) as simple sums over Gaussians, show excellent agreement with the corresponding Hartree-Fock ground-state densities and energies, indicating that this is likely to be a promising method for calculating fairly accurate electron densities in atoms and molecules.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 192
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    International Journal of Quantum Chemistry 23 (1983), S. 71-80 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have shown that integrals Irs and Jrs which occur in coupled Hartree-Fock perturbation, on a basis of gauge invariant atomic orbitals with the London approximation and neglect differential overlap, can be reduced, by appropriate transformations, to the overlap integral type. The computational program of Srs, Irs, and Jrs integrals is elaborated for Slater-type atomic orbitals. The process proposed presents a double advantage: it is extended over the entire Periodical Table and does not use the analytical formulas of Mulliken.
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  • 193
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    International Journal of Quantum Chemistry 23 (1983), S. 85-89 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An idempotent density matrix in which the orbitals are expanded in Bloch sums is used in the density matrix equation for ρ1(1,1′) to obtain an equation appropriate for a crystal. The general equation is presented as well as its simplification for the single-cell approximation and the nearest-neighbor approximation.
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  • 194
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    International Journal of Quantum Chemistry 23 (1983), S. 91-98 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The self-consistent field (SCF) equations for many-electron systems, suitable within the complex-coordinate method, are derived. The formulation is based on a general bivariational theorem for non-Hermitian operators, with an emphasis on the analytic structure invoked by the complex dilation of the total Hamiltonian. The dilation structure of the resulting SCF equations is stressed and the concomitant analytical properties are discussed. The solutions are classified with respect to these properties, and interpreted in terms of a general form of the symmetry dilemma. The role of the dilated SCF equations for resonance calculations is discussed.
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  • 195
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    International Journal of Quantum Chemistry 23 (1983), S. 185-194 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.
    Additional Material: 4 Ill.
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  • 196
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    International Journal of Quantum Chemistry 23 (1983), S. 195-215 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new concept of the “stability” of the quantum mechanical state is presented. This concept is closely related to the hydrodynamical theory of quantum mechanics. For charged particles, the “stability” against the application of the external electromagnetic field is examined. Under a nonlinear interaction, a new type of the solitonlike phenomenon is shown as a novel, illustrative example of the “stable” state. An extension for the relativistic treatment is also examined.
    Additional Material: 3 Ill.
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  • 197
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    International Journal of Quantum Chemistry 23 (1983), S. 169-183 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Unitary transformations are performed with respect to three Lie group chains in quasispin schemes that are involved in the study of three different calculation schemes in ligand field theory. The unitary transformations hold true for either molecular or atomic orbitals being taken as the starting point. As a result, unitary transformations with respect to matrix elements are accomplished as well.
    Additional Material: 6 Tab.
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  • 198
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    International Journal of Quantum Chemistry 23 (1983), S. 257-270 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Local Coulomb correlation hole distribution functions may be used to assess the extent to which electron correlation effects are present in large scale SCF + CI wave functions. From a set of modified virtual orbitals, ordered according to their interaction with the SCF configuration, we have constructed a limited SCF + CI wave function with improved convergence characteristics with respect to that formed from the canonical virtual orbital set. These wave functions, of the same size yet with different energies, have been used to examine the range and depth of local Coulomb correlation holes in FCN. In all cases, the depth of the local Coulomb hole is no more than 10% or so of that of the corresponding Fermi hole, and the range Fermi correlation is generally less than that of Fermi correlation. This is particularly marked in the high density regions around the nuclei. The significance of our results is discussed in relation to a recent proposal for the incorporation of Coulomb correlation into the local exchange method.
    Additional Material: 8 Tab.
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  • 199
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    International Journal of Quantum Chemistry 23 (1983), S. 325-338 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Interaction energies ΔE accompanying the formation of van der Waals (VDW) systems may be estimated by means of the formula ΔE = ΔESCF + BSSE + ED(r-6, r-8, r-10), where BSSE is the basis set superposition error and ED is the dispersion energy in the expanded form. Twenty one stationary points were located on the potential energy surfaces of hydrogen-bonded complexes; of those, 18 were local minima and 3 were saddle points. Thermodynamic characteristics calculated on the basis of molecular constants, quantum chemically generated, were obtained for 12 hydrogen-bonded complexes and for competition equilibria between VDW molecules. The role of the VDW forces in some rate processes and in a prototype of enzyme-substrate interactions is outlined. In connection with enzymic catalysis, the intramolecular discrimination in 1,2-difluorohydrazine, and the stability of hydrogen-bonded complexes in a cation field is discussed.
    Additional Material: 6 Ill.
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  • 200
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    International Journal of Quantum Chemistry 23 (1983), S. 379-385 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The path integral for the Green's function involving the Coulomb potential in combination with the Kustaanheimo-Stiefel transformation is used to generate the atomic orbitals of the nonrelativistic hydrogen atom as various combinations of the product of one-dimensional isotropic harmonic oscillator wave functions. The use of the transformation is justified, by connecting the homogeneous space with the quotient space in the Feynman quantization formalism.
    Type of Medium: Electronic Resource
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